TY - JOUR

T1 - Groupoid C*-Algebras with Hausdorff spectrum

AU - Goehle, Geoff

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2013/10

Y1 - 2013/10

N2 - Suppose that G is a second countable, locally compact Hausdorff groupoid with abelian stabiliser subgroups and a Haar system. We provide necessary and sufficient conditions for the groupoid C* -algebra to have Hausdorff spectrum. In particular, we show that the spectrum of C*(G) is Hausdorff if and only if the stabilisers vary continuously with respect to the Fell topology, the orbit space {G}(0) G is Hausdorff, and, given convergent sequences χi → χ and γi ̇ χi →ω in the dual stabiliser groupoid S where the γi G act via conjugation, if χ and ω are elements of the same fibre then χ = ω.

AB - Suppose that G is a second countable, locally compact Hausdorff groupoid with abelian stabiliser subgroups and a Haar system. We provide necessary and sufficient conditions for the groupoid C* -algebra to have Hausdorff spectrum. In particular, we show that the spectrum of C*(G) is Hausdorff if and only if the stabilisers vary continuously with respect to the Fell topology, the orbit space {G}(0) G is Hausdorff, and, given convergent sequences χi → χ and γi ̇ χi →ω in the dual stabiliser groupoid S where the γi G act via conjugation, if χ and ω are elements of the same fibre then χ = ω.

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U2 - 10.1017/S0004972713000129

DO - 10.1017/S0004972713000129

M3 - Article

AN - SCOPUS:84883639821

SN - 0004-9727

VL - 88

SP - 232

EP - 242

JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

IS - 2

ER -